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An algebraic spin and statistics theorem

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Abstract

A spin-statistics theorem and a PCT theorem are obtained in the context of the superselection sectors in Quantum Field Theory on a 4-dimensional spacetime. Our main assumption is the requirement that the modular groups of the von Neumann algebras of local observables associated with wedge regions act geometrically as pure Lorentz transformations. Such a property, satisfied by the local algebras generated by Wightman fields because of the Bisognano-Wichmann theorem, is regarded as a natural primitive assumption.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, I-00133, Roma, Italia

    Daniele Guido & Roberto Longo

  2. Centro Linceo Interdisciplinare, Accademia Nazionale dei Lincei, via della Lungara 10, I-00165, Roma, Italia

    Roberto Longo

Authors
  1. Daniele Guido
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  2. Roberto Longo
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Additional information

Communicated by H. Araki

Dedicated to Hans Borchers on the occasion of his seventieth birthday

Supported in part by MURST and CNR-GNAFA.

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Guido, D., Longo, R. An algebraic spin and statistics theorem. Commun.Math. Phys. 172, 517–533 (1995). https://doi.org/10.1007/BF02101806

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  • DOI: https://doi.org/10.1007/BF02101806

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